import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import k, m
from proveit.logic import Equals
from proveit.numbers import Exp, Mod, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _alpha_m_mod_two_pow_t, _m_domain, _phase, _two_pow_t
# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = frac(one, _two_pow_t)
sub_expr3 = Exp(e, Mult(two, pi, i, _phase, k))
expr = Equals(Equals(_alpha_m_mod_two_pow_t, Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, Mod(m, _two_pow_t)), _two_pow_t))), sub_expr3), domain = _m_domain))), Equals(_alpha_m_mod_two_pow_t, Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), sub_expr3), domain = _m_domain))))
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
stored_expr.style_options()
# display the expression information
stored_expr.expr_info()